I'll begin with a rough list of various technological achievements by 1 AD:
- The Great Wall of China had already been constructed in whole (by ~100BCE) and part (by ~700 BCE).
- The Romans had constructed aqueducts (312 BCE) and roads (~300BCE).
- The Romans had begun using hydraulic mining in NW Spain by 25BCE.
- The Romans and Chinese had 200 and 300 years of respective experience forging steel.
- The Chinese had 500 years of crossbows.
- Sun Tzu's Art of War was written by 500BCE. (though not a technology it was an impressive and lasting achievement nonetheless)
Note: China wouldn't fully develop gunpowder until Wujing Zongyao was written in 1040-1044 ADE; however, Saltpeter was known to the Chinese by the mid-1st century AD
By well over 1000 BCE Homo Sapiens had already hunted down animals significantly larger than them (Woolly Mammoths, Elephants). As @Resonating noted, we also wiped out large animals on the American Continents. Fastforward to 1ADE and 3 major empires are present:
- Roman Empire under Augustus
- Chinese Han Dynasty
Of them I'll ignore the Parthians since I'm unfamiliar with their history.
BY 1 ADE the Roman Empire had been ruled by Augustus for 28 years. Following "The Transformation", city dwellers would panic over the size of vermin and rural citizens would panic over the size of their cattle or wild animals. The cities would calm rather quickly given the presence of Praetorian Guard, police, and fire fighting established by Augustus and the Roman Legionnaires of course (who happens to include rural farmers in their ranks). Given the large presence of weapons among the populace, I expect they'd make short work of any animals that happens upon them. Deaths by mauling or animal attacks would surely increase; but, this would motivate a systematic response from the Senate and Emperor.
Given their technological prowess, I expect the Romans would construct walls to keep out larger animals. Unlike the Germanic tribes, the Romans would benefit from light sources, horses, roads, and steel/iron weapons. As such, the Germanic tribes would never become a threat to the Romans. Furthermore, given the different chain of events, it's debatable whether Augustus would die when he did (14 AD), especially if Livia did poison him. Considering the Roman Empire's existing domestication and distribution channels the Roman food supply would increase eightfold from meat sources and massively from agriculture (since agriculture would grow to compensate for the animal's increased diet). Furthermore, it's not a stretch to consider how quickly they'd attempt to tame said animals and use them for work or transportation. One of Rome's biggest technological issues was energy sources. With 'The Transformation', every animal they put to work would output 2-8x more energy. How far could a horse 2x taller and longer travel? Imagine how that would affect the Cursus Publicas (also implemented by Augustus)? How would this affect the ability to transport the materials needed to construct walls and aqueducts? This would be a very different Roman Empire without much of the limits that crippled it by 1000 AD.
What is questionable though is the status of their outlying regions (Egypt, Anatolia, Phoenicia, Spain, France). Here I won't speculate (for the moment).
Unlike the Romans, the Chinese are a different beast. By 1 AD they'd mastered warfare and have strongly unified. With the onset of "The Transformation", they'd have the capacity for a rapid response. Since they were quite familiar with East Asia, they'd successfully wage a land war against the animals. I say this because they have strategy, steel weapons, and most importantly: crossbows. Where the Romans have numbers & organization, the Chinese armies would excel in the use of Sun Tzu's stratagems and the skillful application of weapons. Given the knowledge of Salt Peter and China's history of technological advancements during 'war' (namely the warring states period), I have no doubt that they'd develop gunpowder centuries ahead of time.
Yes, Humanity would survive; but, it'd be a vastly different world likely dominated by Rome & China.
- What animals would pose an existential threat to mankind?
- When would the scientific revolution occur in this new world?